Prove that for each $n\geq 3$ the equation: $x^n+y^n+z^n+u^n=v^{n-1}$ has infinitely many solutions in natural numbers.
Problem
Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade
Tags: algebra
Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade
Tags: algebra
Prove that for each $n\geq 3$ the equation: $x^n+y^n+z^n+u^n=v^{n-1}$ has infinitely many solutions in natural numbers.